The man was knocked down on Scotland Road in the Vauxhall area of the city at around 6.50pm.
The victim, who has not yet been identified, was taken to hospital but was pronounced dead shortly after.
A witness told the Liverpool Echo newspaper that the police car had its blue lights flashing at the time of the accident.
Another said the pedestrian was crossing the road when he was hit.
He said: "Two police officers were trying to hold the man.
"I offered them a bottle of water in case they needed it but I didn't want to get in their way."
The incident has been reported to the Independent Office for Police Conduct (IOPC).
A spokesman said: "Merseyside Police has referred to us a fatal collision involving a police car and a pedestrian on Scotland Road in Liverpool this evening.
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"We have sent investigators to the scene.
"Following a brief assessment, we have decided to carry out an independent investigation."